Use Coupon: CART20 and get 20% off on all online Study Material

Total Price: R

There are no items in this cart.
Continue Shopping
Get instant 20% OFF on Online Material.
coupon code: MOB20 | View Course list

  • Complete Physics Course - Class 11
  • OFFERED PRICE: R 2,800
  • View Details
Get extra R 700 off


explain differential equation behind wave motion.

6 years ago


Answers : (1)


Mathematically, the most basic wave is the sine wave (or harmonic wave or sinusoid), with an amplitude u described by the equation:

u(x, \ t)= A \cos (kx - \omega t + \phi) \ ,

where A is the semi-amplitude of the wave, half the peak-to-peak amplitude, often called simply the amplitude – the maximum distance from the highest point of the disturbance in the medium (the crest) to the equilibrium point during one wave cycle. In the illustration to the right, this is the maximum vertical distance between the baseline and the wave; x is the space coordinate, t is the time coordinate, k is the wavenumber (spatial frequency), ω is the temporal frequency, and φ is a phase offset.

The wave equation

The wave equation is a partial differential equation that describes the evolution of a wave over time in a medium where the wave propagates at the same speed independent of wavelength , and independent of amplitude .

consider the wave equation in one dimension, for example, as applied to a string. Suppose a one-dimensional wave is traveling along the x axis with velocity v and amplitude u (which generally depends on both x and t), the wave equation is

\frac{1}{v^2}\frac{\partial^2 u}{\partial  t^2}=\frac{\partial^2 u}{\partial x^2}. \,

The velocity v will depend on the medium through which the wave is moving.

The general solution for the wave equation 

u(x,t)=F(x-vt)+G(x+vt). \,

This formula represents two shapes traveling through the medium in opposite directions; F in the positive x direction, and G in the negative x direction, of arbitrary functional shapes F and G.




6 years ago

Post Your Answer

Other Related Questions on Wave Motion

what is antinode ?
the position of maximum displacement in a standing wave system.
KUNCHAM SAMPATH one year ago
the position of maximum displacement in a standing wave system.
pa1 one year ago
the position of maximum displacement in a standing wave system.
RAKESH CHINDAM one year ago
A piano wire 0.5m long and mass 5gm is streched by a tension of 400N . What is the number of highest overtone that can e heated by a person?
it is a simple substitution problem.. :) f=?, T=400N, l=0.5m, m(=mass/length)=10 -2 as it is a stretched string the highest frequency that can be heard is the fundamental note substitute...
Elton one month ago
1.what is the frequancy of the second on a clock..................................................???????????
Frequency will be 1 by 60 as it comes back to its originial place after 60 second.
Vijay Mukati 9 months ago
dear mani............. The frequency is the inverse of the time period required for the same event to take place again.l ongcase clock with a seconds pendulum. The seconds pendulum, with a...
mohan 9 months ago
Frequency period formula angular frequency cycle per second hertz Hz amplitude equation formulary acoustic time ... Masterclock calculator ( clock rate) .
Gaddam Chethan 9 months ago
What are the units of magnetic moment, magnetic induction and magnetic field
Magnetic moment - Am2(ampere per meter square) Magnetic induction - Tesla(1 gauss = 10 -4 tesla Magnetic field – Tesla
KALYAN 10 months ago
2 bodies A and B has thermal emissivities of 0.01 and 0.81 respectively . The outer surface areas of both bodies are same . Both body emits total radiant power at same rate .The wavelenth...
Let Ta and Tb be the the temp. of A and B. ten, Ta = 3Tb.................(1) And use formulae: Ka x Ta = Kb x Tb where Ka and Kb are the lamdas for A and B respectively. solve the eqns. and ...
Vikas TU 2 months ago
What is single loop circuits?and What is multiloop circuits??????????????????
Gowri Sankar, Single loop: A circuit which has only one loop is called single loop circuits. Multiloop : A circuit which has many loops then it is called multi loop circuits.
SAI SARDAR 9 months ago
A single loop circuit is a circuit in where all elements are connected to form one circuit loop and are connected to atmost two other circuit is called singlelop circuit. a circuit which...
N JYOTHEESWAR 9 months ago
dear gowrishankar, single loop circuits are defined as which has single closed path is called single loop circuits.and which have different closed paths these are called multiloop circuits
Y MANJUNADH 9 months ago
View all Questions »

  • Complete Physics Course - Class 12
  • OFFERED PRICE: R 2,600
  • View Details
Get extra R 650 off

  • Complete Physics Course - Class 11
  • OFFERED PRICE: R 2,800
  • View Details

Get extra R 700 off

More Questions On Wave Motion

Ask Experts

Have any Question? Ask Experts

Post Question

Answer ‘n’ Earn
Attractive Gift
To Win!!!
Click Here for details